International Journal of Engineering Trends and Technology- Volume3Issue2- 2012
Sub-Optimal Estimation of Wind Energy
System through Sub-Division Method
M. Nandana Jyothi# 1, Dr. P. Linga Reddy # 2
1
Asst. Professor, Electrical & Electronics Engineering Department, K. L. University, Guntur-522502, India.
2
Senior Professor, Electrical & Electronics Engineering Department, K. L. University, Guntur-522502, India.
Abstract- This paper presents a new technique, called the
system sub-division method to power train of wind energy
system (WES), the power train of wind energy system is
modeled in state space, and design of kalman filter is used
to estimate the state variables for wind energy system,
which is compared to sub-optimal estimation through
system sub-division method.
Index terms: Kalman filter, MATLAB
I. INTRODUCTION
Wind turbines have become the most costeffective renewable energy systems available today
and are now completely competitive with essentially
all conventional generation systems. However, the
major problem is the wind’s unpredictable nature that
forces utility operators to think differently about
power generation, with the main challenge being to
provide governor functions and controlled ramp
down during high wind speed events. Additionally,
wind turbines present nonlinear dynamic behavior
and lightly damped resonant modes [3].
Concerning reliability, most manufacturers peg the
lifetime of a wind turbine at 20-25 years, and
technological advances in the control system coupled
with pertinent materials for blade strength have
ensured long maintenance-free operation times, and
reduced overheads. The last two arguments focus not
so much on technological challenges but on
aesthetics (visual impact), landscape integration and
transport logistics. Public opposition to facility siting
can be addressed, in part, through development of
novel wind power technologies. Mechanical noise
has practically been eliminated and aerodynamic
noise has been vastly reduced (a WES installation at
350m emits a noise level of35–40 dB, which is
comparable to a quiet indoor room. Wind itself is
noisy!).
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Careful siting can avoid potential interference
with electromagnetic radiation for communication.
Besides, there is evidence from independent studies
suggesting wind farms do not have a significant
adverse effect on AM radio, navigation systems,
mobile phone transmission, and military radar
operation, with the exception of low level air-defense
radar. On the brighter side, there has been
considerable potential created for employment in all
aspects of the wind industry (manufacture, project
design, installation, and O&M), though there are
different ways of estimating the personnel employed
in the wind energy sector.
Overall, the trend towards lower costs for windgenerated electricity has driven manufacturers to less
conservative, more optimized machine design at an
increasingly large scale.
II. WES CONFIGURATION
HAWT/VAWT
Turbine development over the years has
experimented with both horizontal-axis wind turbine
(HAWT) and vertical-axis wind turbine (VAWT)
types. Due to their expected advantages of Omnidirectionality and having gears and generating
equipment at the tower base, vertical axis designs
were considered. However, several disadvantages
have caused the vertical axis design route to
disappear from the mainstream commercial market,
including:
• reduced aerodynamic efficiency — much of the
blade surface is close to the axis
• albeit usually at ground level, it is not feasible to
have the gearbox of large VAWT at ground level
because of the weight and cost of the transmission
shaft
• invariably have a lot of structure per unit of
capacity (centenary curve loaded only in tension).
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International Journal of Engineering Trends and Technology- Volume3Issue2- 2012
There is a continuing tendency to apply many of the
powerful results of modern control theory to the
control and operation of power system. With the
present trends in power systems control requirements,
large size process computers are required to perform
more and more tasks in real time. Since it is difficult
to allocate time and memory on the large size
computer time and storage for the literature which
need less computer time and storage for the
computation of control strategy. Some such methods
are:
1. Reduced order models
2. System decoupling through feedback
3. State vector partitioning and
4. Hierarchical control.
5. System sub-division method
Each method has got its own advantages and
disadvantages. In this paper only the last two
methods are considered to find their suitability for
power system problems and some modifications are
suggested.
In the state vector partitioning method, it is quite
difficult to choose a suitable transformation which
will divide the original system into sub-system,
especially when the size of the system is large. In
order to overcome this problem to study, it is
proposed in this paper to study the applicability of
the canonical transformation due to crossley to divide
the power system into sub-systems. This
transformation is a more formal treatment of the
procedure developed by Luenberger transformation
yields whose dynamic equations are suitable only for
the design of Luenberger type observer for each subsystem and cannot be used directly for the design of
controller and estimator.
• Sub-Optimal Estimation through System SubDivision [1]-[2]— The dynamic equations of the subsystem are modified in this paper so that the subsystem becomes amenable for independent treatment
with regard to the problems of control and estimation.
After making this modification, the control and
estimate for the each sub-system are obtained using
standard optimal control theory and estimation
theory. Then the solution to the problem of control
and estimation in the original system is derived from
the solutions obtained for the sub-system. Since the
sub-systems need only the solutions of lower order
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matrix Riccati equations, there is a considerable
amount of saving in computer time and storage in
case of large power systems through the proposed
method.
In the above methods, state feedback control
requiring knowledge of all the state variables of the
system is employed. In practice, the availability of all
state is rare in which case one has to estimate the
inaccessible states through an estimator. Since the
estimator increases the cost and complexity of the
system, many authors have introduced the design of
output feedback controllers which need only
available outputs of the system for their
implementation. In general, with output feedback
controllers, the stability of the closed loop system is
not guaranteed. In this motivation in mind, an output
feedback controller, which will guarantee the stability
of the system, is also described in this paper.
III. PROBLEM FORMULATION
It deals with a procedure for obtaining the suboptimal state estimates of a system through the
system sub-division method. The sub-optimal
estimate for the large system is determined using the
optimal estimates of the sub-systems. Even though
the estimates of the sub-system are optimal, the
estimates of the original system become sub-optimal
due to the pseudo-inverse involved in the
computations. The sub-optimal estimates are
compared with the optimal estimates computed
through the optimal Kalman-Bucy filter
or the
original system.
Applying the developed methodology of
combining detailed wind turbine subsystems
modeling with a Matlab-Simulink environment for
the analysis of the drive train in wind energy
conversion system, and validation of the developed in
Matlab code. Comparison between actual WES and
sub-optimal estimation through system sub-division
method applied to WES.
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International Journal of Engineering Trends and Technology- Volume3Issue2- 2012
gust is experienced, the system would be subjected to
an instantaneous speed change, Δωt. The dynamics of
the drive train are
Jt
(a) 3- inertia model
Jg
dwt
 d  g
dt
dw g
dt
 g  d
The low speed shaft torque, Γd , acts as braking
torque on the rotor; it results from the torsion and
friction effects due to the difference between speed
of tower ωt and speed of generator ωg and may be
modeled to represent the torsional moments that
relate to the cyclic twist of the shaft during operation


d  K e ( t   g )  D ( wt  wg ) .
(b) 2- inertia model
Fig 1: Dynamic Drive train equivalent system:
rotating masses interlinked by a flexible shaft.
where D represents the damping index and Ke is the
equivalent shaft compliance, given by
IV. STATE SPACE MODEL OF POWER
TRAIN [3]
Fig.1 illustrates the multimass model of the drivetrain, simplified to a spring-mass-damper mechanical
representation. The moments of inertia of the shafts
and the gearbox wheels can be neglected when
assumed to be small compared with either Jt or Jg.
Further, external damping is assumed negligible, and
the moments of inertia of the shafts and the gearbox
wheels can be neglected because they are small
compared with that of the wind turbine or generator.
Therefore the resultant model is essentially a twomass system connected by a flexible shaft of
equivalent stiffness and damping factor (Fig.1(b)).
Only the gearbox ratio has influence on the new
equivalent system [4]
Generally, the drive-train modifies the dynamics
of the system because they include torsional modes
that relate to the aerodynamic rotor mass swinging
with the induction generator mass through the
flexible transmission shaft. In the event that a strong
ISSN: 2231-5381
1
1
1


.
Ke Kt
Kg
N gr2
and further, from Fig. 7.1(b),
tg  (t g ),
dg
dt
 wt , and
 wg
dt
dt
where θt, θg are the angular positions of the shaft at
the rotor and generator sides. In the analysis, Γd is
the torsional torque experienced by the flexible shaft
that couples the two rotating inertias [5].
The linearized model locally valid around the OP
may be developed on an equivalent mathematical
state-space representation of the form
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International Journal of Engineering Trends and Technology- Volume3Issue2- 2012


^
^



z i  Ai z i  H i  y oi  C i z i 


x  Ax  Bu.
y  Cx
where x  _N is a vector consisting of the system
states, u  _M represents the command signals, A
 _N×N is the system matrix while the inputs affect
the state dynamics through the control input B
 _N×M, and Bw  _N×O is the disturbance input
matrix. The output variable y  _P , which is the
measured output (generator speed), is constructed
from the states and the inputs through matrix C
 _P×N. Model orders are defined in {M, N,O, P}.
Note that friction of the shaft at the rotor and
generator sides is implied in D, since the elasticity
and damping elements between the adjacent inertias
correspond to the low- and high-speed shaft
elasticities and internal friction, respectively. The
vector x  _N in (3.6) consists of the system states
defined respectively as follows:
x1 is the perturbed turbine rotor speed,  t
x2 is the perturbed generator speed,  g
x3 is the perturbed shaft torsional torque, d
x4 is the perturbed actuator pitch rate,  , and
x5 is the wind disturbance over the rotor disk, v .


Here
z
i
=estimated state matrix of sub-system.
Ai is state matrix of sub-system.
Ti
y 0i
is transformation matrix of sub-system.
is observations of sub-systems,
H i is sub-optimal kalman gain.
Ci
is output matrx of sub-system.
'
1
Here H i  G i C i Rsi
Gi is the solution of the error covariance matrix
Riccati equation:
Gi Ai'  Ai Gi  Gi Ci' Rsi1Ci Gi  Ti DQs D 'Ti '  0
QS , R S is error covariance matrix;
The combined equations for all sub- system can be
written as:
^
^
^ A1
z1 H1
yo1 C1
z1
z
1



 
0  .  
0  .  
0  . 
.  
^
^ 

^
z 
yoi Ci
z 
Ai
Hi
z
 i 
 i  
  
 i 
0
.
0
.   0


.
 
  
 . 
^
^
^ 







Amz  
Hmyom 
Cmz 
zm 
 m
 m

The state vector transformation matrix is used to
obtain refer [1]-[2]
T
STATE SPACE MODEL OF SYSTEM SUBDIVISION METHOD [1]-[2]
Then the state vector of each sub-system can be
estimated independently. The filter equation of the ith
sub-system can be written as:
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 8.2
T1  
 0

 

T1
T 2



 0.0002 0
 0.00
0
0.00001 0
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0.0049
X10^3 ;
0 
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International Journal of Engineering Trends and Technology- Volume3Issue2- 2012
 8.24
T2   0
 0
 .66
0
0
 0.00
0.005
0.00001 0
0
0
0.0049 
0  X 10^4
.00001
Sub-system-1

8.2 0.0002 0.00 0.00
z1  
0.000001 0.0001 3.0001 0

0.0998
10^3 z 1 + 
 u1
0



y1=
1 0z1
0.0049
0 
H
s
H



1
T 



1
0
H
i
0
H
m



L



L is output transformation matrix.
C 1



1
C L 



0
Ci
0

L'  L1' ....... L'i ....... L'm



T


C m 

sub-system-2
8.24
z2 0
0

0.667 0
0.005 0.0049

0
0
0.0001 0
0
0

0 
0 
0.0998


10 ^ 4 z 2 +  0  u 2 ;
 0 

y2=
0
1 0z 2 ;
Sub Optimal State Estimation Matrix [1]-[2]:
Fig 2: Actual System State Estimations.

^
^



x s  Ax s  H s  y o  C x s  ;



x s is sub-optimal state estimation
Where
 A1



1

Ao  T



0
Ai
0
Am



T



Fig 3: Sub-Division State Estimations
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology- Volume3Issue2- 2012
V. RESULTS
To estimate each state variable of the above
system, the proposed system has been coded in matlab
under without sub-division method, with sub-division
methods and are implemented in Matlab/Simulink.
VI. CONCLUSION
In this paper, sub-division method is used to
estimate the wind energy system. It shows that the
results with the sub-optimal estimation are on par
with the actual system. The saving in computer time
by the system sub-division method is about 28
percent when compared to the time taken for the
without sub-division method, and it saves the
memory also.
VII. REFERENCES
[1] Dr.P.Linga Reddy “some studies on the control
and estimation in power systems through system subdivision”,Ph.D thesis,1977, IIT Delhi.
[2] Dr.P.Linga Reddy and B.S.Rao, “on the control of
large linear system through system sub-division”,
proc.IEE 124 No.8,August 1977, Londan.
[3] Muhando, Billy Endusa Thesis “ Modeling base
intelligent control paradigms modern wind generation
systems”, March, 2008
[4] A. D. Wright, and M. J. Balas, “Design of statespace-based control algorithms for wind turbine
speed regulation,” ASME Journal of Solar Energy
Engineering, vol. 125, no. 4, pp. 386-395, June 2003.
[5] T. Burton, D. Sharpe, N. Jenkins, and E.
Bossanyi, Wind Energy Handbook, New York:
Wiley, 2001. ISBN:978-0471489979.
.
Appendix A [3]
Table A.1: WECS parameters and baseline safety
operational limits
VALUE
Wind turbine and rotor
rated wind speed, vr
12.205 m/s
cut-in/cut-out wind speed
4/25 m/s
gearbox ratio, Kgr
83.33
turbine inertia, Jt
Nm/rad
6.029E+06 kgm2
low speed shaft damping, Ds 1.0E+07 Nms/rad
Generator and grid network
rated capacity, Pr
generator inertia, Jg
2 MW
60 kgm2
max/min generator torque, Γg,
14.4/0 kNm
generator torque set-point
13.4 kN
max/min generator speed
1800/850 rpm
generator stator resistance
0.01 Ω
generator rotor resistance
0.01 Ω
stator leakage inductance
95.5E-06 H
rotor leakage inductance
95.5E-06 H
generator magnetizing (mutual) inductance 0.0955 H
stator rated voltage, Ve
stator rated (electrical) frequency, fn
rotor rated magnetizing current
690 V
50 Hz
1700 A
Pitch controller
max/min pitch angle,
90/-2 deg
max/min pitch rate,
8/-8 deg/s
Table A.2: Performance coefficients calculation
rated wind speed
12.205 m/s
minimum tip-speed ratio
2
maximum tip-speed ratio
20
0.1
blade radius, R
35 m
tip-speed ratio step
number of blades
3
pitch angle
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61.5 m
A.2 Aerodynamics Information
A.1 WES Model Details
PARAMETER
hub height
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-2 deg
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